Question: Simplify the following expression: $ x = \dfrac{-1}{5} + \dfrac{-8k + 9}{-10k} $
In order to add expressions, they must have a common denominator. Multiply the first expression by $\dfrac{-10k}{-10k}$ $ \dfrac{-1}{5} \times \dfrac{-10k}{-10k} = \dfrac{10k}{-50k} $ Multiply the second expression by $\dfrac{5}{5}$ $ \dfrac{-8k + 9}{-10k} \times \dfrac{5}{5} = \dfrac{-40k + 45}{-50k} $ Therefore $ x = \dfrac{10k}{-50k} + \dfrac{-40k + 45}{-50k} $ Now the expressions have the same denominator we can simply add the numerators: $x = \dfrac{10k - 40k + 45}{-50k} $ $x = \dfrac{-30k + 45}{-50k}$ Simplify the expression by dividing the numerator and denominator by -5: $x = \dfrac{6k - 9}{10k}$